text:
Football: Cleverley called into England squad
Manchester United's Tom Cleverley has been called up to the England squad for Wednesday's friendly against the Netherlands.
Arsenal midfielder Jack Wilshere and Manchester United's Michael Carrick have both withdrawn.
Cleverley, 21, came on as a substitute during United's 3-2 Community Shield victory over Manchester City on Sunday.
He has spent most of his United career out on loan, first at Leicester, then at Watford and last season at Wigan.
Cleverley played for England at Under-20 level before making his Under-21 debut against Macedonia in 2009.
United and England team-mate Ashley Young believes the midfielder has a promising future ahead of him.
Young said: "Tom has done terrific all pre-season. He was brilliant when he came on in the Community Shield and he has a great future ahead of him.
"I am sure he will go on to be a top player. He is confident in his own ability and I am sure he will come here and do well."
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redpajama_set_name: RedPajamaCommonCrawl


The announcement yesterday by Britain's Attorney General, Baroness Patricia Scotland, that London's Metropolitan Police are investigating whether officials from the U.K.'s security service, MI5, colluded in the torture of the former Guantánamo prisoner Binyam Mohamed is welcome. It represents a big departure: the first time to date on either side of the Atlantic that civilian intelligence personnel, as opposed to low-level members of the military in places such as Abu Ghraib, have faced criminal sanction for alleged detainee abuse. But whatever its outcome, the case is going to leave big questions unanswered—among them the extent to which the British government, led by former prime minister Tony Blair, signed up to the full program of illegal detention, "extraordinary rendition," and coercive interrogation methods promulgated by the United States in the months after 9/11.
Binyam Mohamed, whose case is described in my 2008 VF.com article "Tortured Reasoning," was captured trying to leave Pakistan with a false passport in April 2002, the start of an almost seven-year odyssey which took him, at the behest of the C.I.A., to detention facilities in Pakistan, Morocco, Afghanistan, and finally Guantánamo. Along the way, as he told me in an interview after his return to Britain at the end of last month, he was beaten, deprived of sleep, suspended from his wrists for days, slashed with a scalpel, and forced to listen to The Eminem Show played at deafening volume 24 hours a day for a month while in total darkness. Documents he acquired as a result of legal proceedings in the United States suggest that MI5 officials either connived in, or at any rate knew about, some of his worst alleged treatment, and I imagine these will provide important leads for the police.
However, the new investigation is not unalloyed good news.
First, it may well prolong the suppression of the redacted sections of a British High Court opinion, which gives a summary of 42 classified C.I.A. documents. These, the court has said, provide details of what exactly did happen to Mohamed, and amount to admissions that he was indeed tortured or subjected to inhuman and degrading treatment. (See my February 2009 VF.com piece, "You Be the Judge.") The British and American media are still fighting to persuade the court to allow publication, and a hearing is due next month. Thus far, to justify prolonging the censorship, Britain's Foreign Secretary, David Miliband, has had to rely on the questionable argument that publication would cause incalculable damage to the U.K.'s intelligence-sharing relationship with America—even though the judges have stated that the redacted sections do not include any secret intelligence material, and even though the Obama administration supposedly has a rather different attitude toward torture than did its predecessor.
The police inquiry may hand Miliband a stronger legal weapon. Britain's laws on what can be published in advance of any criminal trial, or even a possible criminal trial, verge on the draconian. Almost any detail about a suspect's alleged role can be construed as prejudicing the outcome, and to publish such detail is to risk being found in contempt of court. Miliband might well be moved to argue that the redacted material could prejudice the fairness of possible trials involving officials from MI5, and that all argument on the matter must henceforth wait. Even if no one is eventually charged, resolution of the issue would probably take us well past the next U.K. election, which has to take place by June 2010.
Underlying this seems to be a troubling phenomenon: a reluctance in both Britain and America fully to come to terms with the abuses perpetrated by security and intelligence agencies in the "war on terror." As Jane Mayer demonstrates in her book The Dark Side (Doubleday), it is now evident that the worst of these abuses flowed from decisions taken early on, at the highest policy levels; that there was, as the C.I.A.'s former counterterrorist chief, Cofer Black, put it, a shared belief that the only way to stop further mass casualty attacks was to "take the gloves off" when dealing with prisoners. Arguably, to repair the resulting moral damage requires big, public actions—if not trials of those at the top, then perhaps hearings along the lines of South Africa's Truth and Reconciliation Commission. There is little sign of an appetite for anything resembling this. In Britain, publication of Binyam's disclosures did lead some parliamentarians to call for a judicial inquiry into the full extent of the U.K.'s complicity in torture. But most of those who commented on blogs and media Web sites seemed to be concerned not with his treatment but with the fact that, although he is an Ethiopian citizen, albeit long resident in Britain, he has been allowed to stay in the country, instead of being deported.
This lack of outrage is already helping to save Miliband's political career, and it may be helping the cover-up of crimes that go much further than the treatment of one individual. We already know that Britain allowed its Indian Ocean airbase on Diego Garcia to be used as a staging post for C.I.A. rendition flights. I personally have interviewed more than 10 former Guantánamo detainees, both U.K. citizens and residents such as Mohamed: all have alleged U.K. agency complicity in their illegal detention and alleged abusive treatment.
Tony Blair's readiness to follow the Bush administration's lead over Iraq has passed into history. How much did he and his government know about the dark side, and how far did they buy into it?


text:
Gnophos delagardei är en fjärilsart som beskrevs av Louis Beethoven Prout 1915. Gnophos delagardei ingår i släktet Gnophos och familjen mätare. Inga underarter finns listade i Catalogue of Life.

Källor

Mätare
delagardei

redpajama_set_name: RedPajamaWikipedia


text:
\section
In the spontaneous parametric downconversion (SPDC) process, portion of pump photons split into photon pairs created with energies strictly satisfying the energy conservation condition and scattered in directions promoted by the momentum conservation (or phase-matching) condition.
The SPDC photons are thus entangled by nature in energy-time \cite{hong1987measurement,franson1989bell} as well as in momentum-position \cite{mair2001entanglement,lima2006propagation,barbieri2007complete, walborn2010spatial,leach2010quantum}. However for the polarization, the remaining degree of freedom (DoF), its entanglement appears always as a consequence of subtle designs using either a single \cite{kwiat1995new,Hugues2006non,kim2006phase,ueno2012entangled} or more nonlinear crystals \cite{kwiat1999ultrabright,kim2001interferometric,ljunggren2006theory,hegazy2017orthogonal,Villar2018Experimental}.

In either case, the wavefunctions of the two polarization possibilities (HH and VV for $|\phi^\pm\rangle$, or HV and VH for $|\psi^\pm\rangle$) can be made almost identical in magnitude, while a comprehensive picture about the indistinguishability in the space and time domains is provided by the directional-spectral relative-phase function. Generally, a flatter relative-phase function in some domain implies higher indistinguishability in its conjugate Fourier-transform domain
 \cite{hegazy2017orthogonal,Hegazy2017CLEO}.
Therefore, the spatial and temporal compensations actually correct (or flatten) the varying relative-phase function in direction and frequency. Several works previously addressed spatial and temporal compensations at specific spatial modes \cite{kwiat1995new,nambu2002generation,ljunggren2006theory,trojek2008collinear} or over relatively narrow aperture \cite{altepeter2005phase,rangarajan2009optimizing,cialdi2010programmable} by the use of additional birefringent elements.
Over such limited spatial extents, well-designed birefringent elements can effectively clean for the linear dependence of the relative phase function and restore the indistinguishability \cite{hegazy2015tunable}.
This is not the case when photon pairs are collected over relatively wide angular extents, where higher-order contributions of the relative-phase function drastically
reduce the effectiveness of linear methods.

In this paper, we present and demonstrate experimentally a method for eliminating the spatial and temporal distinguishability of a polarization-entangled state over wide emission angles.
We initially derive the two-photon state emitted by a noncollinear SPDC; including the directional-spectral relative-phase function all over the SPDC cone.
It is noticed that while the time-delay map (the spatial distribution of spectral relative-phase gradient) has a negligible change over wide angular extent, the directional relative-phase exhibits obvious quadratic profile. To restore the temporal and spatial indistinguishability, the compensation of the former can be effectively done in the conventional way; using a birefringent element. The latter is manipulated using a two-dimensional spatial light modulator (2D SLM) loaded with the inverted relative-phase profile. A fast yet accurate experimental technique is introduced to directly measure the relative-phase profile; dispensing with the quantum state tomography.

Consider a diagonally polarized pump beam illuminating a couple of crossed type-I crystals which are identically cut to promote production of degenerate photons in a noncollinear SPDC geometry.
The pump beam is classically treated as a superposition of frequency and plane-wave  modes:
$E_{{p}}(\mathbf{x},z,t)= \int d\omega _{{p}}d\mathbf{q}_{{p}}~A_{p}(\omega_{{p}};\mathbf{q} _{{p}})\exp i\left(\kappa _{{p}}z+\mathbf{q}_{{p}}. \mathbf{x}-\omega _{{p}}t\right) +\mathrm{c.c.}$,
with angular frequency $\omega _{p}$ and wavevector $\mathbf{k}_{p}=(%
\mathbf{q}_{{p}},\kappa _{{p}})$ where $\mathbf{q}_{{p}%
} $ are the transverse components along the coordinates $\mathbf{x}=(x,y)$, and $\kappa _{p}$ is the longitudinal component.
The pump polarization components in horizontal/vertical (H/V) basis have a relative phase $\phi_p$ that can be manipulated by tilting a birefringent element; e.g., a quarter wave plate (QWP).

Similarly, the produced SPDC two-photon emission can be expressed –based on the SPDC creation operators– as a joint spectral and spatial expansion in monochromatic planar waves with the angular frequencies $\omega_{1,2}$ and the transverse wave vectors  $\mathbf{q}_{\mathrm{1,2}}$ (subscripts 1, 2 denote signal and idler photons, respectively).
The longitudinal wavevectors of the interacting waves can be expressed as dictated by Maxwell's equations for ordinary (\textit{o}) and extraordinary (\textit{e}) polarization as
\cite{born2013principles,walborn2010spatial,hegazy2017orthogonal}
\begin{equation}
\begin{split}
&\kappa _{{j}}^{o }(\omega_{{j}};\mathbf{q}_{{j}})=\sqrt{( {\omega_{{j}} ~n_{{j}}^{o}}/{c}) ^{2}-\vert \mathbf{q}_{{j}}\vert
^{2}}\\
&\kappa _j ^{e(H,V)}(\omega_j;\mathbf{q}_j)
=   q_{j(x,y)} \tan\rho^\perp_j \\
&~~~~~~~~~~~~+ n_j^{e^\perp} \left[ \left(\tfrac{\omega _j}{c} \right) ^{2} -         \tfrac{1}{(n_j^e)^2}   q_{j(y,x)}^2-       (\tfrac{{n_j^{e^\perp}}}{n_j^e n_j^o} )^2         q_{j(x,y)}^2 \right]^{\frac{1}{2}},\\
\end{split}
\label{eq:Longwavevector}
\end{equation}
where the subscript $j=p, 1, 2$, the superscripts $(H)$ and $(V)$ label the SPDC crystals with optic axes lying in the $xz$ (horizontal) and $yz$ (vertical) plane respectively, $c$ is the speed of light in space, $n_{{j}}^{o}$ and $n_{{j}}^{e}$ are principal values of refractive index, and $n_j^{e^\perp}$ and $\rho^\perp_j$ are  the refractive indices and walk-off angles of the extraordinary-polarized ray propagating along $z$ axis (perpendicular to the crystals interfaces).
The SPDC in the two crystals creates a two-photon state entangled in every degree of freedom; frequency, momentum, and polarization, which is expressed at small emission angles  \cite{migdall1997polarization} by the superposition
\begin{equation}
\begin{split}
\left\vert \psi \right\rangle   \sim  \mathbf{\int}d\omega _{1}d\omega _{2}d\mathbf{q}_{1}d%
\mathbf{q}_{2} &{\large \{}\Phi _\mathrm{HH}\left(\omega _{1},\omega _{2};\mathbf{q}%
_{1},\mathbf{q}_{2}\right)\left\vert H_1H_2
\right\rangle \\
&+~\Phi _\mathrm{VV}\left( \omega _{1},\omega
_{2};\mathbf{q}_{1},\mathbf{q}_{2}\right) \left\vert V_1V_2
\right\rangle{\large \}},
\end{split}
\label{ent1}
\end{equation}
where $\Phi _\mathrm{HH,VV}\left(\omega _{1},\omega _{2};\mathbf{q}_{1},\mathbf{q}_{2}\right)$ are the biphoton wavefunctions corresponding to the HH and VV possibilities.
 Assuming that the crystals are of infinite transverse extent and pumped by a non-depleted beam with the reflected waves at all crystal interfaces being negligible, the two-photon wavefunctions can be written as
\begin{equation*}
\begin{split}
\Phi_\mathrm{HH} = ~&\tfrac{\chi^{(2)}}{\sqrt[]{2}} A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) \int_{-2L}^{-L} dz~ e^{i \int_0^z dz^{\prime } \Delta \kappa(z^{\prime })}, \\
\propto ~&
e^{-i L\left(\tfrac{1}{2}{\Delta \kappa_{V}^{ooe}} + \Delta \kappa_H^{eeo}  \right)}
L
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) ~ \mathrm{sinc} \left( \tfrac{ \Delta \kappa_{V}^{ooe} L}{2}\right), \\
\Phi_\mathrm{VV} = ~&  e^{-i\phi_p}~ \tfrac{\chi^{(2)}}{\sqrt[]{2}}
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) \int_{-L}^{0} dz~ e^{i \int_0^z dz^{\prime } \Delta \kappa(z^{\prime })}, \\
\propto ~&
 e^{-i\left(\phi_p+\tfrac{1}{2}{\Delta \kappa_{H}^{ooe}L} \right)}
L
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2)  ~\mathrm{sinc} \left(\tfrac{\Delta \kappa_{H}^{ooe} L}{2}\right), \\
\end{split}
\label{Eq: amplitudes}
\end{equation*}
where
$L$ is the crystal length, $\chi ^{(2)}$ is the bilinear susceptibility,
$~\Delta \kappa^{ooe}_{H,V} =\kappa _{p}^{e(H,V)}-\kappa _{1}^{o}-\kappa _{2}^{o}$ are  wavevector mismatches  within the interacting $(H)$ and $(V)$ crystals,
$\Delta \kappa_H^{eeo}=\kappa _{p}^{o}-\kappa _{1}^{e(H)}-\kappa_{2}^{e(H)}$ is the mismatch of waves interacting in the first crystal when passing through the second one ($\Delta \kappa_H^{eeo} \gg \Delta \kappa^{ooe}_{H,V}$, therefore no downconversion is considered in the later case).

The relative phase of the produced state $|\psi\rangle$ is then
\begin{equation}
\begin{split}
\vartheta
=\mathsf{arg}\left\{  \Phi_\mathrm{VV} / \Phi_\mathrm{HH} \right\}=
\left[\tfrac{1}{2}({\Delta \kappa_{V}^{ooe} }-\Delta \kappa_{H}^{ooe}) + \Delta \kappa_H^{eeo}  \right] L -\phi_p,
\end{split}
\label{eq:relative_phase}
\end{equation}
which includes phase-matching terms and an initial phase term. We assume that the spatiotemporal amplitude of the pump beam is factorizable:
$A_p(\omega_p;\mathbf{q}_p)= ({\sqrt[]{\tau_p}}/{\sqrt[4]{\pi}})\,\exp [-\tfrac{1}{2} \tau_p^2 (\omega_{{p}}-\omega_p^0)^2 ] \,\,\, \delta(\mathbf{q}_p),$ which expresses a polychromatic plane wave with a coherence time $\tau_p$. Therefore, the biphoton spatial characteristics can be fully determined with reference to the signal photon alone ($\mathbf{q}_2 = -\mathbf{q}_1$). This assumption implies also that $\Delta \kappa_{V}^{ooe} \approx\Delta \kappa_{H}^{ooe}\equiv\Delta \kappa^{ooe}$ as dictated by Eq. (\ref{eq:Longwavevector}); and consequently $|\Phi_\mathrm{HH}|\approx|\Phi_\mathrm{VV}|$. By substituting Eq. (\ref{eq:Longwavevector}) into Eq. (\ref{eq:relative_phase}) and ignoring the insignificant higher-order terms, the relative phase writes
\begin{equation}
\begin{split}
    \vartheta  (\omega _{1},\omega _{2};  \mathbf{q}_{1},  & -\mathbf{q}_{1}) \approx\\
\Big \{ & \frac{(n_p^o - n_1^{e^\perp}) \omega_1 + (n_p^o -  n_2^{e^\perp}) \omega_2}{c}\\
&- q_{1,x} (\tan \rho_1^\perp   -   \tan \rho_2^\perp ) \\
&+  \frac{c q_{1,x}^2}{2}    \Big[ \frac{(n_1^{e^\perp})^3}{\omega_1  (n_1^e )^2 (n_1^o)^2}  + \frac{(n_2^{e^\perp} )^3}{\omega_2  (n_2^e )^2 (n_2^o )^2}\Big] \\
&+ \frac{c q_{1,y}^2}{2} \Big[ \frac{n_1^{e^\perp}}{\omega_1 (n_1^e )^2} + \frac{n_2^{e^\perp}}{\omega_2 (n_2^e )^2 }\Big] \Big\} L - \phi_p,
\end{split}
\label{eq:relative_phase_approx}
\end{equation}
which is a quadratic function in the transverse wavevector components of the SPDC photons.
 Moreover, the first-order derivatives of the relative phase $\vartheta$ with respect to $\omega_1$ and $\omega_2$ determine the time delay \textit{map} between HH and VV possibilities for the signal and idler photons, respectively [that is, for a biphoton emission in the directions specified by $(\mathbf{q}_{1},-\mathbf{q}_{1})$]. Equation (\ref{eq:relative_phase_approx}) thus presents closed forms for the relative-phase and time-delay maps which give theoretical predictions equivalent to those of the iterative approach given in Ref. \cite{hegazy2017relative}. For convenience, the components of $\mathbf{q}_1$ are substituted by the free-space emission angles in $xz$ (horizontal) and $yz$ (vertical) planes as $q_{1x,y}= \tan \theta_{x1,y1}~\sqrt[]{(\omega_1/c)^2-|\mathbf{q}_1|^2}$ (similarly, $\mathbf{q}_2$).

\begin{figure*} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=12cm]{setup_station6}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:setup}
Extended entangled-photons source. The photon pairs are created in two crossed type-I 0.5-mm BBO crystals cut at 29.3$^\mathsf{o}$ and pumped by 405-nm beam to produce noncollinear SPDC photons centered at ~3$^\mathsf{o}$ half-opening angle. A half-wave plate (HWP$_p$) and a tiltable quarter-wave plate (QWP$_p$) manipulate the pump polarization state and are also components of polarization interferometer used for relative-phase measurements.
The relative-phase function is manipulated in frequency using a temporal compensator (TC), and in direction via a two-dimenstional spatial light modulator (2D SLM) charged by the inverted grayscale relative-phase map. PM: Partial mirror; D: Classical detector; APD: Avalanche photodiode, IF: interference filter, L: lens.
}
\end{figure*}

The coincidence map, on the other hand, is determined by the two-photon wavefunction at the detection plane \cite{klyshko1988photons}
\begin{equation}
\begin{split}
\Psi
=\langle 0 | E_1^{(+)}(\theta_{x1},\theta_{y1};t_1) E_2^{(+)}(\theta_{x2},\theta_{y2};t_2) |\psi \rangle, \\
\end{split}
\end{equation}
where $|0\rangle$ is the vacuum state and
\begin{equation*}
\begin{split}
& E_{1}^{(+)
=\int d\omega~e^{-i\omega t_{1}} \sum_{\mathbf{\sigma}}
(\mathbf{e}_1 . \mathbf{\sigma}) G(\omega)~ \mathbf{a}_\mathbf{\sigma}(\omega;\theta_{x1},\theta_{y1}), \\
& E_{2}^{(+)
=\int d\omega~ e^{-i\omega t_{2}}  \sum_{\mathbf{\sigma}}
(\mathbf{e}_2 . \mathbf{\sigma}) G(\omega)~ \mathbf{a}_\mathbf{\sigma}(\omega;\theta_{x2},\theta_{y2}),
\end{split}
\end{equation*}
are the positive-frequency parts of signal and idler field operators at the space-time coordinates of biphoton detection; $(\theta_{x1},\theta_{y1};t_{1})$ and $(\theta_{x2},\theta_{y2};t_{2})$ \cite{saleh2000duality}. Here the unit vector $\mathbf{e}_i=(e_{ix},e_{iy})$ specifies the orientation of the polarization analyzer in the $i$th SPDC arm, $G(.)$ is the transmissivity profile of the spectral filters, and $\mathbf{a}_\sigma(\omega; \theta_{x},\theta_{y})$ is the photon annihilation operator for a mode of frequency $\omega$, polarization $\mathbf{\sigma}$, and direction defined by the emission angles $(\theta_{x},\theta_{y})$ in free space. The spatiotemporal two-photon wavefunction thus writes \cite{atature2002multiparameter}
\begin{equation}
\begin{split}
\Psi
= \frac{1}{2} \mathbf{\int}&d\omega _{1}d\omega _{2}
  e^{-i(\omega_1 t_1 + \omega_2 t_2)}
\\
\times & G(\omega_1) G(\omega_2) \left( e_{1x}e_{2x}\Phi _\mathrm{HH}+ e_{1y}e_{2y} \Phi _\mathrm{VV} \right),
\end{split}
\label{Eq:DetectedWavefn}
\end{equation}
and the probability that the signal photon is captured by the typically used slow-response detector in the direction $(\theta_{x1},\theta_{y1})$ is then given by
\begin{equation}
P(\theta_{x1},\theta_{y1})=\int dt_1 dt_2 d\theta_{x2} d\theta_{y2}|\Psi (\theta_{x1},\theta_{y1},\theta_{x2},\theta_{y2}; t_1, t_2)|^2.
\label{Eq:angdistribution}
\end{equation}

 The schematic of the experimental setup is shown in Fig. \ref{fig:setup}. A collimated 405-nm beam emitted by a continuous-wave diode laser with $\sim$300-fs coherence time is used to pump two abutted 0.5-mm type-I BBO crystals with the optic axis of the first (second) crystal lying in the vertical (horizontal) plane. The two crystals are anti-reflection-coated at all wavelengths of concern and cut at 29.3$^\mathsf{o}$ to produce degenerate SPDC cone centered at ~3$^\mathsf{o}$ half-opening angle.
 The polarizing beam splitter (PBS) improves the extinction ratio of the pump beam (from 20:1 to about 10000:1). The half-wave plate (HWP$_p$) and tiltable quarter-wave plate (QWP$_p$) manipulate the pump polarization state –by rotating the linear polarization and adding phase difference $\phi_p$, respectively– and are also used to conduct the phase measurements as follows.
 To determine the phase difference $\phi_p$, the partial mirror (PM) back-reflects a tiny portion ($\sim 2\%$) of the pump beam to be analyzed by the dash-outlined polarization interferometer.
 At its output, the normalized optical power measured by the classical detector (D) is proportionate to $\sin^2 \phi_p$ (see supplementary material). We used 10-nm interference filters centered at 810 nm. This narrowband detection at the degenerate frequency along with the collimated-beam pumping render the approximations: $\theta_{x1}\approx - \theta_{x2}$ and $\theta_{y1}\approx - \theta_{y2}$ reasonable. We will henceforth refer to $\theta_{x1}$ and $\theta_{y1}$ as  $\theta_{x}$ and $\theta_{y}$, respectively, for short.

\begin{figure*} [t]

   \hspace{- .5cm}
   \centering
   \includegraphics[width=17cm]{Exp_ang_coincidence_two0-5BBO_2_polari_11-12}
   \caption[example]
   { \label{fig:coincidence}

Coincidence and time-delay maps all over the SPDC cone.
(a) Theoretical prediction (left) and experimental measurements (right) for the angular distribution of biphotons coincidence counts after polarization projection into the diagonal basis state $|++\rangle$. The right inset shows the normalized coincidence rates (red points), experimentally measured behind a 2-mm iris positioned, 50 cm from the SPDC crystals, at the directions: $\theta_x=\{2.4^\mathsf{o}, 2.7^\mathsf{o}, 3^\mathsf{o}, 3.3^\mathsf{o}, 3.45^\mathsf{o}, 3.6^\mathsf{o}\};$ with $\theta_y=0$.  The yellow line shows the normalized rates as predicted by Eq. (\ref{Eq:angdistribution}). (b) The same as in (a) after polarization projection into the rectilinear basis state $|HH\rangle$.
(c) The directional time-delay map between the HH and VV possibilities for the degenerate biphoton emission as predicted by the derivative of the relative phase $\vartheta$ with respect to $\omega_1$.}
   \end{figure*}

In the experiment, to figure out the spatial distribution of the scattered biphotons, the coincidence counts are measured behind a 2-mm circular iris translated laterally at $\sim$50 cm from the SPDC crystals. The measurements are made at a number of transverse positions which represent one radial group.
 Figure \ref{fig:coincidence}(a) shows the coincidence counts recorded after polarization projection into the basis state $|++\rangle$. We noticed that this spatial distribution varied when polarization projection was performed with different orientation. Figure \ref{fig:coincidence}(b) shows the coincidence counts after polarization projection into the basis state $|HH\rangle$ which exhibits more angular spread than that of the diagonal projection. This observation is in good agreement with Eq. (\ref{Eq:DetectedWavefn}) and Eq. (\ref{Eq:angdistribution}), where for the projector $|HH\rangle\langle HH|$, $e_{1x}e_{2x}=1$ and $e_{1y}e_{2y}=0$, which yields angular distribution $P(\theta_{x},\theta_{y})\propto \mathrm{sinc}^2 \left(\Delta \kappa^{ooe} L/2\right)$. Alternatively, for the diagonal projector $|++\rangle\langle ++|$, the factors $e_{1x}e_{2x}=e_{1y}e_{2y}=1/2$, therefore $P(\theta_{x},\theta_{y})\propto \mathrm{sinc}^2 \left(\Delta \kappa^{ooe} L/2\right) \cos^2 (\vartheta/2)$. The more confined angular distribution in case of diagonal projection originates from the interference of SPDC biphotons created along the two crystals. This observation shows one side of the coupling effects between polarization and spatial DoFs which can be eliminated via a suitable spatial phase compensation.

Figure \ref{fig:coincidence}(c) and Figure \ref{fig:phasemap}(a) show the time-delay and relative-phase maps all over the SPDC scattering cone as obtained by Eq. (\ref{eq:relative_phase_approx}) for the parameters of the experiment.
It can be noticed that while the time-delay map is essentially flat (centered at $\sim$200 fs), the relative-phase map has strong quadratic dependence in the radial direction.
This time delay is about the same as the coherence time of the SPDC light (determined by the interference filters). Therefore, over that wide directional extent, the temporal distinguishability between the leading (HH) and the lagging (VV) possibilities can be effectively washed out following the conventional approach; adding an offset temporal delay between the parent pump components $|V_p\rangle$ and  $|H_p\rangle$ \cite{nambu2002generation,rangarajan2009optimizing,hegazy2015tunable}.
In the experiment, this is accomplished using a temporal compensator (TC): Two \textit{available} 0.8-mm 30$^\mathsf{o}$-cut BBO crystals set abutted to each other with their optic axes rotated up-side-down  with respect to each other in the vertical plane; thereby canceling the transverse walk-off. To verify the degree of temporal compensation, we measured the visibility of coincidence fringes after 2-mm iris while HWP$_1$ is rotated and HWP$_2$ remains fixed at $22.5^\mathsf{o}$.
High polarization visibility was observed at all the transverse positions in Fig. \ref{fig:coincidence}; implying the flatness of the time-delay map and the effectiveness of the unified time compensation.

 At each observation point, the high polarization visibility was achievable at a tilt angle of QWP$_p$ different from its neighboring points (thus, different $\phi_p$). This indicates that the phase-matching part of the relative phase in Eq. (\ref{eq:relative_phase}) varies from a point to another.

 \begin{figure} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=8.5cm]{phase_theta_pe_0_phi_pe_0_shortened_6}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:phasemap}
(a) The two-dimensional quadratic relative-phase map (in radians) as predicted by Eq. (\ref{eq:relative_phase_approx}) all over the SPDC cone.  (b) Purifying SLM pattern to produce the states $|\phi^\pm\rangle$ with high fidelity over wide emission angles. The pattern constitutes the inverted \textit{modulo-2$\pi$} grayscale of the map in (a). The white rectangle circumscribes the 2D SLM's active area on which the compensation image is loaded. This area covers azimuthal-angle range $\sim$57$^\mathsf{o}$ (of the 180$^\mathsf{o}$ representing half SPDC cone); therefore about one  third  of  the  noncollinear SPDC emission cone could be manipulated.  (c) Experimentally measured phase retardation introduced by the 8-bit SLM at 810 nm plotted versus the gray display level (black:0 and white:255). The phase measurement error ($\pm 0.005 \pi$) is smaller than the readout markers.
}
   \end{figure}

Based on this observation, we present here an experimental technique to directly measure the relative phase of the entangled state:
First, polarization measurements are prepared projecting the two-photon state to diagonal basis states $|++\rangle, $ $|--\rangle$. We then scan the tilt angle of QWP$_p$. Along the scan, reaching the maximum coincidence counts indicates constructing a state nearest to the Bell state: $|\phi^+\rangle= (|H_1H_2\rangle+|V_1V_2\rangle)/\sqrt{2}$ [Here, the zero relative phase indicates that the phase-matching part of the relative phase is complementary to $\phi_p$ as dictated by Eq. (\ref{eq:relative_phase})] \cite{note:auto}. This determines the phase-matching part of the relative phase, since $\phi_p$ value is obtained from the normalized power detected by the photodetector D as aforementioned (see supplementary material).

To compensate for the relative-phase variation, a phase-only two-dimensional spatial light modulator (2D SLM) in one of the SPDC arms is used to introduce a pixel-based phase retardation between the H and V polarization components.
This reflective 2D SLM (display area 15.36 mm$\times$8.64 mm and resolution 1920$\times$1080 pixels) is placed at the transverse plane, $\sim$24.4  cm  from  the  SPDC  crystals, and programmed by a personal computer (PC). After loading by a grayscale image, the SLM develops a phase retardation for each pixel proportional to the pixel's gray level as commonly used in the monochromatic digital display.
The SLM can introduce up to $\sim 2\pi$ phase shift at 810 nm with its  8-bit display offering 256 intermediate gray/phase levels (black:0 and white:255).
 To treat the relative-phase map, the SLM was charged by the image within the white rectangle in Fig. \ref{fig:phasemap}(b) which is the inverted grayscale image of the modulo-2$\pi$ relative-phase map in Fig. \ref{fig:phasemap}(a). Figure \ref{fig:phasemap}(c) shows the experimentally measured phase of the SLM for the display gray levels \{0 (black), 63, 127, 192, 255 (white)\}.
 A special gamma correction is applied to enhance the linearity of the phase retardation to the pixel gray level at 810 nm.
Figure \ref{fig:measuredPhase_gradient} depicts the experimentally measured relative phase at the transverse positions in Fig. \ref{fig:coincidence} before and after charging the SLM with the compensating image.
The improved flatness of the directional relative-phase function implies less coupling between polarization and spatial DoFs. This yields polarization-entangled state $|\phi^+\rangle$ with high fidelity verified by $\sim 97\%$ polarization visibility measured at all transverse positions in Fig. \ref{fig:coincidence} across the SPDC emission (see supplementary material). This high visibility of coincidence fringes was observed at each  position behind the 2-mm iris while HWP$_1$ was rotated, with HWP$_2$ fixed at $22.5^\mathsf{o}$, and QWP$_p$ set at fixed tilting. By tilting QWP$_p$, the extended high-fidelity emission of the state $|\phi^-\rangle$ could also be formed.
   \begin{figure} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=8.5 cm]{Experimental_Phase_both_5}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:measuredPhase_gradient}
Experimentally measured relative phase for the produced polarization-entangled state across the SPDC cone before (brown rhombuses) and after (blue squares) loading the SLM. The measurements are done behind a 2-mm iris positioned, 50 cm from the SPDC crystals, at the directions: $\theta_x=\{2.7^\mathsf{o}, 3^\mathsf{o}, 3.3^\mathsf{o}, 3.45^\mathsf{o}, 3.6^\mathsf{o}\};$ with $\theta_y=0$. The error ($\pm 0.005 \pi$) is smaller than the symbols. Curves are fits to the data.
}
   \end{figure}

Beside equalizing the quadratic relative phase, the PC-programmed 2D SLM can simultaneously superimpose phase patterns serving other DoFs (e.g., orbital angular momentum modulation/demodulation). However, the following factors have to be taken into account:
(i) The SLM introduces unavoidable loss factor that can be classified as bulk losses due to the non-ideal reflectivity/transmissivity and diffraction losses due to the pixelation splitting of the incident light into several diffraction orders. In our experiment, the SLM losses reached $\sim 40 \%$. (ii) Effective anti-reflection coating is essential to diminish the possibility that the photon is not manipulated (by reflecting off the first interface) or manipulated multiple times (by rebouncing across the SLM).

To sum up, we have presented an experimental method to compensate for the spatial-spectral relative-phase function of a polarization entangled state, and produce the maximally entangled states $|\phi^\pm\rangle$ with high fidelity over wide emission angle –involving one third of the SPDC cone.
 In frequency domain, the relative-phase gradient has been treated conventionally by the use of unified temporal compensator.
In momentum domain, the relative phase over extended emission angles exhibits obvious two-dimensional quadratic dependence which has been equalized by using a high resolution PC-programmed 2D SLM loaded by the inverted relative-phase function. We have also developed a simple, yet accurate, experimental approach to measuring the relative phase of the entangled photon pairs by witnessing a normalized portion of the emerging power of the pump beam after polarization interferometry.
The high visibility and flat relative phase of the constructed state has been verified in a set of lateral positions across the SPDC cone. The presented approach can be applied to equalize the entire SPDC emission by using 2D SLM of sufficiently wide active area covering half the SPDC emission cone. Furthermore, the Bell states $|\psi^\pm\rangle$ –extended over wide angles– can be straightforwardly produced by inserting a half-wave plate \cite{note:waveplate} into one SPDC arm.
\\

See supplementary material for further information
about the relative-phase measurement technique and visibility measurements.
\\

This work is supported by ITAC program (Grant No. CFP134), ITIDA, Ministry of Communications and Information Technology (MCIT), Egypt.\\
\\
\noindent\textbf{Data Availability}

The data that supports the findings of this study are available within the article and its supplementary material.

\section
In the spontaneous parametric downconversion (SPDC) process, portion of pump photons split into photon pairs created with energies strictly satisfying the energy conservation condition and scattered in directions promoted by the momentum conservation (or phase-matching) condition.
The SPDC photons are thus entangled by nature in energy-time \cite{hong1987measurement,franson1989bell} as well as in momentum-position \cite{mair2001entanglement,lima2006propagation,barbieri2007complete, walborn2010spatial,leach2010quantum}. However for the polarization, the remaining degree of freedom (DoF), its entanglement appears always as a consequence of subtle designs using either a single \cite{kwiat1995new,Hugues2006non,kim2006phase,ueno2012entangled} or more nonlinear crystals \cite{kwiat1999ultrabright,kim2001interferometric,ljunggren2006theory,hegazy2017orthogonal,Villar2018Experimental}.

In either case, the wavefunctions of the two polarization possibilities (HH and VV for $|\phi^\pm\rangle$, or HV and VH for $|\psi^\pm\rangle$) can be made almost identical in magnitude, while a comprehensive picture about the indistinguishability in the space and time domains is provided by the directional-spectral relative-phase function. Generally, a flatter relative-phase function in some domain implies higher indistinguishability in its conjugate Fourier-transform domain
 \cite{hegazy2017orthogonal,Hegazy2017CLEO}.
Therefore, the spatial and temporal compensations actually correct (or flatten) the varying relative-phase function in direction and frequency. Several works previously addressed spatial and temporal compensations at specific spatial modes \cite{kwiat1995new,nambu2002generation,ljunggren2006theory,trojek2008collinear} or over relatively narrow aperture \cite{altepeter2005phase,rangarajan2009optimizing,cialdi2010programmable} by the use of additional birefringent elements.
Over such limited spatial extents, well-designed birefringent elements can effectively clean for the linear dependence of the relative phase function and restore the indistinguishability \cite{hegazy2015tunable}.
This is not the case when photon pairs are collected over relatively wide angular extents, where higher-order contributions of the relative-phase function drastically
reduce the effectiveness of linear methods.

In this paper, we present and demonstrate experimentally a method for eliminating the spatial and temporal distinguishability of a polarization-entangled state over wide emission angles.
We initially derive the two-photon state emitted by a noncollinear SPDC; including the directional-spectral relative-phase function all over the SPDC cone.
It is noticed that while the time-delay map (the spatial distribution of spectral relative-phase gradient) has a negligible change over wide angular extent, the directional relative-phase exhibits obvious quadratic profile. To restore the temporal and spatial indistinguishability, the compensation of the former can be effectively done in the conventional way; using a birefringent element. The latter is manipulated using a two-dimensional spatial light modulator (2D SLM) loaded with the inverted relative-phase profile. A fast yet accurate experimental technique is introduced to directly measure the relative-phase profile; dispensing with the quantum state tomography.

Consider a diagonally polarized pump beam illuminating a couple of crossed type-I crystals which are identically cut to promote production of degenerate photons in a noncollinear SPDC geometry.
The pump beam is classically treated as a superposition of frequency and plane-wave  modes:
$E_{{p}}(\mathbf{x},z,t)= \int d\omega _{{p}}d\mathbf{q}_{{p}}~A_{p}(\omega_{{p}};\mathbf{q} _{{p}})\exp i\left(\kappa _{{p}}z+\mathbf{q}_{{p}}. \mathbf{x}-\omega _{{p}}t\right) +\mathrm{c.c.}$,
with angular frequency $\omega _{p}$ and wavevector $\mathbf{k}_{p}=(%
\mathbf{q}_{{p}},\kappa _{{p}})$ where $\mathbf{q}_{{p}%
} $ are the transverse components along the coordinates $\mathbf{x}=(x,y)$, and $\kappa _{p}$ is the longitudinal component.
The pump polarization components in horizontal/vertical (H/V) basis have a relative phase $\phi_p$ that can be manipulated by tilting a birefringent element; e.g., a quarter wave plate (QWP).

Similarly, the produced SPDC two-photon emission can be expressed –based on the SPDC creation operators– as a joint spectral and spatial expansion in monochromatic planar waves with the angular frequencies $\omega_{1,2}$ and the transverse wave vectors  $\mathbf{q}_{\mathrm{1,2}}$ (subscripts 1, 2 denote signal and idler photons, respectively).
The longitudinal wavevectors of the interacting waves can be expressed as dictated by Maxwell's equations for ordinary (\textit{o}) and extraordinary (\textit{e}) polarization as
\cite{born2013principles,walborn2010spatial,hegazy2017orthogonal}
\begin{equation}
\begin{split}
&\kappa _{{j}}^{o }(\omega_{{j}};\mathbf{q}_{{j}})=\sqrt{( {\omega_{{j}} ~n_{{j}}^{o}}/{c}) ^{2}-\vert \mathbf{q}_{{j}}\vert
^{2}}\\
&\kappa _j ^{e(H,V)}(\omega_j;\mathbf{q}_j)
=   q_{j(x,y)} \tan\rho^\perp_j \\
&~~~~~~~~~~~~+ n_j^{e^\perp} \left[ \left(\tfrac{\omega _j}{c} \right) ^{2} -         \tfrac{1}{(n_j^e)^2}   q_{j(y,x)}^2-       (\tfrac{{n_j^{e^\perp}}}{n_j^e n_j^o} )^2         q_{j(x,y)}^2 \right]^{\frac{1}{2}},\\
\end{split}
\label{eq:Longwavevector}
\end{equation}
where the subscript $j=p, 1, 2$, the superscripts $(H)$ and $(V)$ label the SPDC crystals with optic axes lying in the $xz$ (horizontal) and $yz$ (vertical) plane respectively, $c$ is the speed of light in space, $n_{{j}}^{o}$ and $n_{{j}}^{e}$ are principal values of refractive index, and $n_j^{e^\perp}$ and $\rho^\perp_j$ are  the refractive indices and walk-off angles of the extraordinary-polarized ray propagating along $z$ axis (perpendicular to the crystals interfaces).
The SPDC in the two crystals creates a two-photon state entangled in every degree of freedom; frequency, momentum, and polarization, which is expressed at small emission angles  \cite{migdall1997polarization} by the superposition
\begin{equation}
\begin{split}
\left\vert \psi \right\rangle   \sim  \mathbf{\int}d\omega _{1}d\omega _{2}d\mathbf{q}_{1}d%
\mathbf{q}_{2} &{\large \{}\Phi _\mathrm{HH}\left(\omega _{1},\omega _{2};\mathbf{q}%
_{1},\mathbf{q}_{2}\right)\left\vert H_1H_2
\right\rangle \\
&+~\Phi _\mathrm{VV}\left( \omega _{1},\omega
_{2};\mathbf{q}_{1},\mathbf{q}_{2}\right) \left\vert V_1V_2
\right\rangle{\large \}},
\end{split}
\label{ent1}
\end{equation}
where $\Phi _\mathrm{HH,VV}\left(\omega _{1},\omega _{2};\mathbf{q}_{1},\mathbf{q}_{2}\right)$ are the biphoton wavefunctions corresponding to the HH and VV possibilities.
 Assuming that the crystals are of infinite transverse extent and pumped by a non-depleted beam with the reflected waves at all crystal interfaces being negligible, the two-photon wavefunctions can be written as
\begin{equation*}
\begin{split}
\Phi_\mathrm{HH} = ~&\tfrac{\chi^{(2)}}{\sqrt[]{2}} A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) \int_{-2L}^{-L} dz~ e^{i \int_0^z dz^{\prime } \Delta \kappa(z^{\prime })}, \\
\propto ~&
e^{-i L\left(\tfrac{1}{2}{\Delta \kappa_{V}^{ooe}} + \Delta \kappa_H^{eeo}  \right)}
L
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) ~ \mathrm{sinc} \left( \tfrac{ \Delta \kappa_{V}^{ooe} L}{2}\right), \\
\Phi_\mathrm{VV} = ~&  e^{-i\phi_p}~ \tfrac{\chi^{(2)}}{\sqrt[]{2}}
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2) \int_{-L}^{0} dz~ e^{i \int_0^z dz^{\prime } \Delta \kappa(z^{\prime })}, \\
\propto ~&
 e^{-i\left(\phi_p+\tfrac{1}{2}{\Delta \kappa_{H}^{ooe}L} \right)}
L
A_p(\omega_1+\omega_2;\mathbf{q}_1+\mathbf{q}_2)  ~\mathrm{sinc} \left(\tfrac{\Delta \kappa_{H}^{ooe} L}{2}\right), \\
\end{split}
\label{Eq: amplitudes}
\end{equation*}
where
$L$ is the crystal length, $\chi ^{(2)}$ is the bilinear susceptibility,
$~\Delta \kappa^{ooe}_{H,V} =\kappa _{p}^{e(H,V)}-\kappa _{1}^{o}-\kappa _{2}^{o}$ are  wavevector mismatches  within the interacting $(H)$ and $(V)$ crystals,
$\Delta \kappa_H^{eeo}=\kappa _{p}^{o}-\kappa _{1}^{e(H)}-\kappa_{2}^{e(H)}$ is the mismatch of waves interacting in the first crystal when passing through the second one ($\Delta \kappa_H^{eeo} \gg \Delta \kappa^{ooe}_{H,V}$, therefore no downconversion is considered in the later case).

The relative phase of the produced state $|\psi\rangle$ is then
\begin{equation}
\begin{split}
\vartheta
=\mathsf{arg}\left\{  \Phi_\mathrm{VV} / \Phi_\mathrm{HH} \right\}=
\left[\tfrac{1}{2}({\Delta \kappa_{V}^{ooe} }-\Delta \kappa_{H}^{ooe}) + \Delta \kappa_H^{eeo}  \right] L -\phi_p,
\end{split}
\label{eq:relative_phase}
\end{equation}
which includes phase-matching terms and an initial phase term. We assume that the spatiotemporal amplitude of the pump beam is factorizable:
$A_p(\omega_p;\mathbf{q}_p)= ({\sqrt[]{\tau_p}}/{\sqrt[4]{\pi}})\,\exp [-\tfrac{1}{2} \tau_p^2 (\omega_{{p}}-\omega_p^0)^2 ] \,\,\, \delta(\mathbf{q}_p),$ which expresses a polychromatic plane wave with a coherence time $\tau_p$. Therefore, the biphoton spatial characteristics can be fully determined with reference to the signal photon alone ($\mathbf{q}_2 = -\mathbf{q}_1$). This assumption implies also that $\Delta \kappa_{V}^{ooe} \approx\Delta \kappa_{H}^{ooe}\equiv\Delta \kappa^{ooe}$ as dictated by Eq. (\ref{eq:Longwavevector}); and consequently $|\Phi_\mathrm{HH}|\approx|\Phi_\mathrm{VV}|$. By substituting Eq. (\ref{eq:Longwavevector}) into Eq. (\ref{eq:relative_phase}) and ignoring the insignificant higher-order terms, the relative phase writes
\begin{equation}
\begin{split}
    \vartheta  (\omega _{1},\omega _{2};  \mathbf{q}_{1},  & -\mathbf{q}_{1}) \approx\\
\Big \{ & \frac{(n_p^o - n_1^{e^\perp}) \omega_1 + (n_p^o -  n_2^{e^\perp}) \omega_2}{c}\\
&- q_{1,x} (\tan \rho_1^\perp   -   \tan \rho_2^\perp ) \\
&+  \frac{c q_{1,x}^2}{2}    \Big[ \frac{(n_1^{e^\perp})^3}{\omega_1  (n_1^e )^2 (n_1^o)^2}  + \frac{(n_2^{e^\perp} )^3}{\omega_2  (n_2^e )^2 (n_2^o )^2}\Big] \\
&+ \frac{c q_{1,y}^2}{2} \Big[ \frac{n_1^{e^\perp}}{\omega_1 (n_1^e )^2} + \frac{n_2^{e^\perp}}{\omega_2 (n_2^e )^2 }\Big] \Big\} L - \phi_p,
\end{split}
\label{eq:relative_phase_approx}
\end{equation}
which is a quadratic function in the transverse wavevector components of the SPDC photons.
 Moreover, the first-order derivatives of the relative phase $\vartheta$ with respect to $\omega_1$ and $\omega_2$ determine the time delay \textit{map} between HH and VV possibilities for the signal and idler photons, respectively [that is, for a biphoton emission in the directions specified by $(\mathbf{q}_{1},-\mathbf{q}_{1})$]. Equation (\ref{eq:relative_phase_approx}) thus presents closed forms for the relative-phase and time-delay maps which give theoretical predictions equivalent to those of the iterative approach given in Ref. \cite{hegazy2017relative}. For convenience, the components of $\mathbf{q}_1$ are substituted by the free-space emission angles in $xz$ (horizontal) and $yz$ (vertical) planes as $q_{1x,y}= \tan \theta_{x1,y1}~\sqrt[]{(\omega_1/c)^2-|\mathbf{q}_1|^2}$ (similarly, $\mathbf{q}_2$).

\begin{figure*} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=12cm]{setup_station6}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:setup}
Extended entangled-photons source. The photon pairs are created in two crossed type-I 0.5-mm BBO crystals cut at 29.3$^\mathsf{o}$ and pumped by 405-nm beam to produce noncollinear SPDC photons centered at ~3$^\mathsf{o}$ half-opening angle. A half-wave plate (HWP$_p$) and a tiltable quarter-wave plate (QWP$_p$) manipulate the pump polarization state and are also components of polarization interferometer used for relative-phase measurements.
The relative-phase function is manipulated in frequency using a temporal compensator (TC), and in direction via a two-dimenstional spatial light modulator (2D SLM) charged by the inverted grayscale relative-phase map. PM: Partial mirror; D: Classical detector; APD: Avalanche photodiode, IF: interference filter, L: lens.
}
\end{figure*}

The coincidence map, on the other hand, is determined by the two-photon wavefunction at the detection plane \cite{klyshko1988photons}
\begin{equation}
\begin{split}
\Psi
=\langle 0 | E_1^{(+)}(\theta_{x1},\theta_{y1};t_1) E_2^{(+)}(\theta_{x2},\theta_{y2};t_2) |\psi \rangle, \\
\end{split}
\end{equation}
where $|0\rangle$ is the vacuum state and
\begin{equation*}
\begin{split}
& E_{1}^{(+)
=\int d\omega~e^{-i\omega t_{1}} \sum_{\mathbf{\sigma}}
(\mathbf{e}_1 . \mathbf{\sigma}) G(\omega)~ \mathbf{a}_\mathbf{\sigma}(\omega;\theta_{x1},\theta_{y1}), \\
& E_{2}^{(+)
=\int d\omega~ e^{-i\omega t_{2}}  \sum_{\mathbf{\sigma}}
(\mathbf{e}_2 . \mathbf{\sigma}) G(\omega)~ \mathbf{a}_\mathbf{\sigma}(\omega;\theta_{x2},\theta_{y2}),
\end{split}
\end{equation*}
are the positive-frequency parts of signal and idler field operators at the space-time coordinates of biphoton detection; $(\theta_{x1},\theta_{y1};t_{1})$ and $(\theta_{x2},\theta_{y2};t_{2})$ \cite{saleh2000duality}. Here the unit vector $\mathbf{e}_i=(e_{ix},e_{iy})$ specifies the orientation of the polarization analyzer in the $i$th SPDC arm, $G(.)$ is the transmissivity profile of the spectral filters, and $\mathbf{a}_\sigma(\omega; \theta_{x},\theta_{y})$ is the photon annihilation operator for a mode of frequency $\omega$, polarization $\mathbf{\sigma}$, and direction defined by the emission angles $(\theta_{x},\theta_{y})$ in free space. The spatiotemporal two-photon wavefunction thus writes \cite{atature2002multiparameter}
\begin{equation}
\begin{split}
\Psi
= \frac{1}{2} \mathbf{\int}&d\omega _{1}d\omega _{2}
  e^{-i(\omega_1 t_1 + \omega_2 t_2)}
\\
\times & G(\omega_1) G(\omega_2) \left( e_{1x}e_{2x}\Phi _\mathrm{HH}+ e_{1y}e_{2y} \Phi _\mathrm{VV} \right),
\end{split}
\label{Eq:DetectedWavefn}
\end{equation}
and the probability that the signal photon is captured by the typically used slow-response detector in the direction $(\theta_{x1},\theta_{y1})$ is then given by
\begin{equation}
P(\theta_{x1},\theta_{y1})=\int dt_1 dt_2 d\theta_{x2} d\theta_{y2}|\Psi (\theta_{x1},\theta_{y1},\theta_{x2},\theta_{y2}; t_1, t_2)|^2.
\label{Eq:angdistribution}
\end{equation}

 The schematic of the experimental setup is shown in Fig. \ref{fig:setup}. A collimated 405-nm beam emitted by a continuous-wave diode laser with $\sim$300-fs coherence time is used to pump two abutted 0.5-mm type-I BBO crystals with the optic axis of the first (second) crystal lying in the vertical (horizontal) plane. The two crystals are anti-reflection-coated at all wavelengths of concern and cut at 29.3$^\mathsf{o}$ to produce degenerate SPDC cone centered at ~3$^\mathsf{o}$ half-opening angle.
 The polarizing beam splitter (PBS) improves the extinction ratio of the pump beam (from 20:1 to about 10000:1). The half-wave plate (HWP$_p$) and tiltable quarter-wave plate (QWP$_p$) manipulate the pump polarization state –by rotating the linear polarization and adding phase difference $\phi_p$, respectively– and are also used to conduct the phase measurements as follows.
 To determine the phase difference $\phi_p$, the partial mirror (PM) back-reflects a tiny portion ($\sim 2\%$) of the pump beam to be analyzed by the dash-outlined polarization interferometer.
 At its output, the normalized optical power measured by the classical detector (D) is proportionate to $\sin^2 \phi_p$ (see supplementary material). We used 10-nm interference filters centered at 810 nm. This narrowband detection at the degenerate frequency along with the collimated-beam pumping render the approximations: $\theta_{x1}\approx - \theta_{x2}$ and $\theta_{y1}\approx - \theta_{y2}$ reasonable. We will henceforth refer to $\theta_{x1}$ and $\theta_{y1}$ as  $\theta_{x}$ and $\theta_{y}$, respectively, for short.

\begin{figure*} [t]

   \hspace{- .5cm}
   \centering
   \includegraphics[width=17cm]{Exp_ang_coincidence_two0-5BBO_2_polari_11-12}
   \caption[example]
   { \label{fig:coincidence}

Coincidence and time-delay maps all over the SPDC cone.
(a) Theoretical prediction (left) and experimental measurements (right) for the angular distribution of biphotons coincidence counts after polarization projection into the diagonal basis state $|++\rangle$. The right inset shows the normalized coincidence rates (red points), experimentally measured behind a 2-mm iris positioned, 50 cm from the SPDC crystals, at the directions: $\theta_x=\{2.4^\mathsf{o}, 2.7^\mathsf{o}, 3^\mathsf{o}, 3.3^\mathsf{o}, 3.45^\mathsf{o}, 3.6^\mathsf{o}\};$ with $\theta_y=0$.  The yellow line shows the normalized rates as predicted by Eq. (\ref{Eq:angdistribution}). (b) The same as in (a) after polarization projection into the rectilinear basis state $|HH\rangle$.
(c) The directional time-delay map between the HH and VV possibilities for the degenerate biphoton emission as predicted by the derivative of the relative phase $\vartheta$ with respect to $\omega_1$.}
   \end{figure*}

In the experiment, to figure out the spatial distribution of the scattered biphotons, the coincidence counts are measured behind a 2-mm circular iris translated laterally at $\sim$50 cm from the SPDC crystals. The measurements are made at a number of transverse positions which represent one radial group.
 Figure \ref{fig:coincidence}(a) shows the coincidence counts recorded after polarization projection into the basis state $|++\rangle$. We noticed that this spatial distribution varied when polarization projection was performed with different orientation. Figure \ref{fig:coincidence}(b) shows the coincidence counts after polarization projection into the basis state $|HH\rangle$ which exhibits more angular spread than that of the diagonal projection. This observation is in good agreement with Eq. (\ref{Eq:DetectedWavefn}) and Eq. (\ref{Eq:angdistribution}), where for the projector $|HH\rangle\langle HH|$, $e_{1x}e_{2x}=1$ and $e_{1y}e_{2y}=0$, which yields angular distribution $P(\theta_{x},\theta_{y})\propto \mathrm{sinc}^2 \left(\Delta \kappa^{ooe} L/2\right)$. Alternatively, for the diagonal projector $|++\rangle\langle ++|$, the factors $e_{1x}e_{2x}=e_{1y}e_{2y}=1/2$, therefore $P(\theta_{x},\theta_{y})\propto \mathrm{sinc}^2 \left(\Delta \kappa^{ooe} L/2\right) \cos^2 (\vartheta/2)$. The more confined angular distribution in case of diagonal projection originates from the interference of SPDC biphotons created along the two crystals. This observation shows one side of the coupling effects between polarization and spatial DoFs which can be eliminated via a suitable spatial phase compensation.

Figure \ref{fig:coincidence}(c) and Figure \ref{fig:phasemap}(a) show the time-delay and relative-phase maps all over the SPDC scattering cone as obtained by Eq. (\ref{eq:relative_phase_approx}) for the parameters of the experiment.
It can be noticed that while the time-delay map is essentially flat (centered at $\sim$200 fs), the relative-phase map has strong quadratic dependence in the radial direction.
This time delay is about the same as the coherence time of the SPDC light (determined by the interference filters). Therefore, over that wide directional extent, the temporal distinguishability between the leading (HH) and the lagging (VV) possibilities can be effectively washed out following the conventional approach; adding an offset temporal delay between the parent pump components $|V_p\rangle$ and  $|H_p\rangle$ \cite{nambu2002generation,rangarajan2009optimizing,hegazy2015tunable}.
In the experiment, this is accomplished using a temporal compensator (TC): Two \textit{available} 0.8-mm 30$^\mathsf{o}$-cut BBO crystals set abutted to each other with their optic axes rotated up-side-down  with respect to each other in the vertical plane; thereby canceling the transverse walk-off. To verify the degree of temporal compensation, we measured the visibility of coincidence fringes after 2-mm iris while HWP$_1$ is rotated and HWP$_2$ remains fixed at $22.5^\mathsf{o}$.
High polarization visibility was observed at all the transverse positions in Fig. \ref{fig:coincidence}; implying the flatness of the time-delay map and the effectiveness of the unified time compensation.

 At each observation point, the high polarization visibility was achievable at a tilt angle of QWP$_p$ different from its neighboring points (thus, different $\phi_p$). This indicates that the phase-matching part of the relative phase in Eq. (\ref{eq:relative_phase}) varies from a point to another.

 \begin{figure} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=8.5cm]{phase_theta_pe_0_phi_pe_0_shortened_6}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:phasemap}
(a) The two-dimensional quadratic relative-phase map (in radians) as predicted by Eq. (\ref{eq:relative_phase_approx}) all over the SPDC cone.  (b) Purifying SLM pattern to produce the states $|\phi^\pm\rangle$ with high fidelity over wide emission angles. The pattern constitutes the inverted \textit{modulo-2$\pi$} grayscale of the map in (a). The white rectangle circumscribes the 2D SLM's active area on which the compensation image is loaded. This area covers azimuthal-angle range $\sim$57$^\mathsf{o}$ (of the 180$^\mathsf{o}$ representing half SPDC cone); therefore about one  third  of  the  noncollinear SPDC emission cone could be manipulated.  (c) Experimentally measured phase retardation introduced by the 8-bit SLM at 810 nm plotted versus the gray display level (black:0 and white:255). The phase measurement error ($\pm 0.005 \pi$) is smaller than the readout markers.
}
   \end{figure}

Based on this observation, we present here an experimental technique to directly measure the relative phase of the entangled state:
First, polarization measurements are prepared projecting the two-photon state to diagonal basis states $|++\rangle, $ $|--\rangle$. We then scan the tilt angle of QWP$_p$. Along the scan, reaching the maximum coincidence counts indicates constructing a state nearest to the Bell state: $|\phi^+\rangle= (|H_1H_2\rangle+|V_1V_2\rangle)/\sqrt{2}$ [Here, the zero relative phase indicates that the phase-matching part of the relative phase is complementary to $\phi_p$ as dictated by Eq. (\ref{eq:relative_phase})] \cite{note:auto}. This determines the phase-matching part of the relative phase, since $\phi_p$ value is obtained from the normalized power detected by the photodetector D as aforementioned (see supplementary material).

To compensate for the relative-phase variation, a phase-only two-dimensional spatial light modulator (2D SLM) in one of the SPDC arms is used to introduce a pixel-based phase retardation between the H and V polarization components.
This reflective 2D SLM (display area 15.36 mm$\times$8.64 mm and resolution 1920$\times$1080 pixels) is placed at the transverse plane, $\sim$24.4  cm  from  the  SPDC  crystals, and programmed by a personal computer (PC). After loading by a grayscale image, the SLM develops a phase retardation for each pixel proportional to the pixel's gray level as commonly used in the monochromatic digital display.
The SLM can introduce up to $\sim 2\pi$ phase shift at 810 nm with its  8-bit display offering 256 intermediate gray/phase levels (black:0 and white:255).
 To treat the relative-phase map, the SLM was charged by the image within the white rectangle in Fig. \ref{fig:phasemap}(b) which is the inverted grayscale image of the modulo-2$\pi$ relative-phase map in Fig. \ref{fig:phasemap}(a). Figure \ref{fig:phasemap}(c) shows the experimentally measured phase of the SLM for the display gray levels \{0 (black), 63, 127, 192, 255 (white)\}.
 A special gamma correction is applied to enhance the linearity of the phase retardation to the pixel gray level at 810 nm.
Figure \ref{fig:measuredPhase_gradient} depicts the experimentally measured relative phase at the transverse positions in Fig. \ref{fig:coincidence} before and after charging the SLM with the compensating image.
The improved flatness of the directional relative-phase function implies less coupling between polarization and spatial DoFs. This yields polarization-entangled state $|\phi^+\rangle$ with high fidelity verified by $\sim 97\%$ polarization visibility measured at all transverse positions in Fig. \ref{fig:coincidence} across the SPDC emission (see supplementary material). This high visibility of coincidence fringes was observed at each  position behind the 2-mm iris while HWP$_1$ was rotated, with HWP$_2$ fixed at $22.5^\mathsf{o}$, and QWP$_p$ set at fixed tilting. By tilting QWP$_p$, the extended high-fidelity emission of the state $|\phi^-\rangle$ could also be formed.
   \begin{figure} [t]
   \begin{center}
   \begin{tabular}{c}
   \includegraphics[width=8.5 cm]{Experimental_Phase_both_5}
   \end{tabular}
   \end{center}
   \caption[example]
   { \label{fig:measuredPhase_gradient}
Experimentally measured relative phase for the produced polarization-entangled state across the SPDC cone before (brown rhombuses) and after (blue squares) loading the SLM. The measurements are done behind a 2-mm iris positioned, 50 cm from the SPDC crystals, at the directions: $\theta_x=\{2.7^\mathsf{o}, 3^\mathsf{o}, 3.3^\mathsf{o}, 3.45^\mathsf{o}, 3.6^\mathsf{o}\};$ with $\theta_y=0$. The error ($\pm 0.005 \pi$) is smaller than the symbols. Curves are fits to the data.
}
   \end{figure}

Beside equalizing the quadratic relative phase, the PC-programmed 2D SLM can simultaneously superimpose phase patterns serving other DoFs (e.g., orbital angular momentum modulation/demodulation). However, the following factors have to be taken into account:
(i) The SLM introduces unavoidable loss factor that can be classified as bulk losses due to the non-ideal reflectivity/transmissivity and diffraction losses due to the pixelation splitting of the incident light into several diffraction orders. In our experiment, the SLM losses reached $\sim 40 \%$. (ii) Effective anti-reflection coating is essential to diminish the possibility that the photon is not manipulated (by reflecting off the first interface) or manipulated multiple times (by rebouncing across the SLM).

To sum up, we have presented an experimental method to compensate for the spatial-spectral relative-phase function of a polarization entangled state, and produce the maximally entangled states $|\phi^\pm\rangle$ with high fidelity over wide emission angle –involving one third of the SPDC cone.
 In frequency domain, the relative-phase gradient has been treated conventionally by the use of unified temporal compensator.
In momentum domain, the relative phase over extended emission angles exhibits obvious two-dimensional quadratic dependence which has been equalized by using a high resolution PC-programmed 2D SLM loaded by the inverted relative-phase function. We have also developed a simple, yet accurate, experimental approach to measuring the relative phase of the entangled photon pairs by witnessing a normalized portion of the emerging power of the pump beam after polarization interferometry.
The high visibility and flat relative phase of the constructed state has been verified in a set of lateral positions across the SPDC cone. The presented approach can be applied to equalize the entire SPDC emission by using 2D SLM of sufficiently wide active area covering half the SPDC emission cone. Furthermore, the Bell states $|\psi^\pm\rangle$ –extended over wide angles– can be straightforwardly produced by inserting a half-wave plate \cite{note:waveplate} into one SPDC arm.
\\

See supplementary material for further information
about the relative-phase measurement technique and visibility measurements.
\\

This work is supported by ITAC program (Grant No. CFP134), ITIDA, Ministry of Communications and Information Technology (MCIT), Egypt.\\
\\
\noindent\textbf{Data Availability}

The data that supports the findings of this study are available within the article and its supplementary material.

redpajama_set_name: RedPajamaArXiv


text:
Q: Yii2 GridView change sort icons I have installed yii2,I want to change GridView Sort icons and class.
How I can do this? I searched in yii2 documentation but nothing found.
Yii2 Grid Code:
<?php echo GridView::widget([
'dataProvider' => $dataProvider,
'filterModel' => $searchModel,
'columns' => [
    ['class' => 'yii\grid\SerialColumn'],

        [
            'attribute' => 'createdate',
            'label' => Yii::t('app', 'Created'),
            'value' => function ($data) { return '4 September 2013'; },
        ],

    ...

    ['class' => 'yii\grid\ActionColumn'],
  ],
]);

A: Change your web/css/site.css as below for ascending order(use desc for descending order). Use your own icon url.
a.asc:after {
content: url(link/to/images/img.jpg);
}

Use the below to add class to your cell
'contentOptions' => ['class' => 'come-class']

A: try create your own class extend ActionColumn
class myActionColumn extends ActionColumn {
    public function initDefaultButtons()
    {
        if (!isset($this->buttons['view'])) {
            $this->buttons['view'] = function ($url, $model, $key) {
                $options = array_merge([
                    'title' => Yii::t('yii', 'View'),
                    'aria-label' => Yii::t('yii', 'View'),
                    'data-pjax' => '0',
                ], $this->buttonOptions);
                return Html::a('', $url, $options);
            };
        }
        if (!isset($this->buttons['update'])) {
            $this->buttons['update'] = function ($url, $model, $key) {
                $options = array_merge([
                    'title' => Yii::t('yii', 'Update'),
                    'aria-label' => Yii::t('yii', 'Update'),
                    'data-pjax' => '0',
                ], $this->buttonOptions);
                return Html::a('', $url, $options);
            };
        }
        if (!isset($this->buttons['delete'])) {
            $this->buttons['delete'] = function ($url, $model, $key) {
                $options = array_merge([
                    'title' => Yii::t('yii', 'Delete'),
                    'aria-label' => Yii::t('yii', 'Delete'),
                    'data-confirm' => Yii::t('yii', 'Are you sure you want to delete this item?'),
                    'data-method' => 'post',
                    'data-pjax' => '0',
                ], $this->buttonOptions);
                return Html::a('', $url, $options);
            };
        }
    }
}

and change what you need and use this class instead of ActionColumn class

A: ** You can simply add a always visible sort icon by using this script - please check pjax is used if not modify function call according**
$script = <<< JS
    var removeSortIcon = function(event) {
            $('[data-sort]').each(function() {
                var element = $(this);
                if(element.hasClass('desc') || element.hasClass('asc') ){
                    element.remove('span');
                }else{
                    element.append(' ');
                }
            });
    }
    $(document).ready(removeSortIcon);
    $(document).on('ready pjax:success', removeSortIcon);
JS;
$this->registerJs($script);

Second way :
 $dataProvider = new ActiveDataProvider([
        'query' => $query,
        'sort' => [
            'defaultOrder' => ['name' => SORT_ASC,'email' => SORT_ASC,'username' => SORT_ASC,],
        ],
  ]);

redpajama_set_name: RedPajamaStackExchange


text:
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[ January 20, 2020 ] Newly-Elected Patriarch of Turkey Lashes Back at his Armenian Critics	My Turn
[ January 19, 2020 ] ARS Announces its Spring 2020 Norian Youth Connect Program	Nonprofit News
[ January 18, 2020 ] Reflections on the Baku and Sumgait Pogroms: 30 Years Later	Nonprofit News
[ January 18, 2020 ] AMAA-Armenia Obtains Belarus Tractor for Navur Cooperative of Tavush Region	Nonprofit News
[ January 18, 2020 ] AMAA Shares the Joy of Christmas with over 11,000 Children Throughout Armenia, Artsakh	News
4,500 Guests Attend Special Armenian Genocide Program in Kremlin Hall
March 2, 2016 at 1:18 pm Harut Sassounian My Turn 1
The 10th annual Armenian Music Awards (AMA) were held on Feb. 27 at the Kremlin's Kevorkiev Hall in Moscow, with 4,500 guests in attendance. Many of Armenia's top stars entertained the large crowd with patriotic songs and musical performances for more than four hours.
This year's program, organized by Valeriy Saharyan, recognized the important contributions made by 12 individuals and organizations on the occasion of the Armenian Genocide Centennial, including:
– Vladimir Zhirinovsky (member of the Russian Parliament)
– Harut Sassounian (publisher of the California Courier and President of Armenia Artsakh Fund)
– Armenia Futura
– Sergey Smpatian (conductor)
Other honorees, some of whom could not be present, appeared by video or through a representative:
– Valerie Boyer (member of the French Parliament)
– Vigen Sargsyan (Armenian president's chief of staff and coordinator of programs organized by the State Centennial Committee of the Armenian Genocide)
– Armenia's minister of culture
– Archbishop Ezras Nercessian (Primate of Moscow and Nor Nakhichevan)
– Serj Tankian ("System of a Down")
– Rouben Vartanian (benefactor and businessman)
– Artur Janipekyan (Gazprom Media Holding)
– Ara Vartanyan (Hayastan All-Armenian Fund)
In receiving his award, Zhirinovsky had strong words for Turkey: "The day will come when Armenians will celebrate their festivals in the territory of liberated Western Armenia. That could be a festival bearing the name of your holy mountain—Mount Ararat—and could take place in Kars, Ardahan, Sassoun or Trabizon. … After the downing of the Russian jet, I would have ordered a powerful attack on Turkey. Today, very little would have remained of Turkey. … I wish the dream of Armenians worldwide would become a reality, that those who committed that horrible genocide on April 1915, during World War I, would be punished."
Zhirinovsky continued his aggressive words, stating that Turkey attacked the Armenians who "were living in their homeland, in their land. But the Turks were nomads; their homeland is in Central Asia, in Tashkent. They should go there and leave Anatolia to Armenians, Kurds, and Greeks. And Constantinople should be a free city. Times are changing. It is possible that shortly this would become a reality. Armenians, no one will bother you. Therefore, the descendants of Western Armenia should prepare their documents to get back their lost lands and properties. I am not talking a lot of 'hot air.' I am convinced that Armenians will shortly commemorate not the anniversary of the Armenian Genocide, but celebrate the liberation of Western Armenia. And the Armenian flag will fly in Kars, Ardahan, on Ararat, Sassoun, and Trabzon."
I had a hard act to follow after Zhirinovsky's powerful words. In accepting my award, I made the following brief remarks:
"Genocide is a monstrous crime which has no statutes of limitations. The Turkish government should well know that the Armenian nation will never give up its just rights. Although 100 years have passed, even if 1,000 years should pass, we will continue to demand, and struggle to regain everything that we lost. Turkey must return all our personal and communal properties—and more importantly—our historic lands of Western Armenia. In other words, we demand our confiscated possessions, and compensation for the murder of our 1.5 million holy martyrs."
I then urged the audience not to despair: "One hundred years ago, the powerful and vast Ottoman Empire collapsed and broke apart, turning into the Republic of Turkey within much smaller borders. With God's help and our persistent efforts, I am convinced that the day will come when today's Turkey would also collapse due to internal and external pressures. We must be prepared to take advantage of such an opportunity to liberate our historic lands. Until then, Armenia, Artsakh, and the diaspora should be united into one fist, so that our homeland would become a strong economic, political, and military power. Only such a powerful Armenia can take ownership of its just rights rather than begging for them."
This uplifting four-hour program was broadcast live by Armenia's public television to Armenian communities throughout the world. I am confident that the 4,500 guests at the Kremlin Hall and millions of TV viewers felt a renewed sense of determination to pursue their national goals until their eventual realization.
California Courier Editor
Harut Sassounian is the publisher of The California Courier, a weekly newspaper based in Glendale, Calif. He is the president of the United Armenian Fund, a coalition of the seven largest Armenian-American organizations. He has been decorated by the president and prime minister of the Republic of Armenia, and the heads of the Armenian Apostolic and Catholic churches. He is also the recipient of the Ellis Island Medal of Honor.
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Gurgen says:
Thank you for this wonderful news Mr Sassounian. God Bless Russia and Vladimir Putin.
Newly-Elected Patriarch of Turkey Lashes Back at his Armenian Critics
January 20, 2020 at 8:03 pm 3
ARS Announces its Spring 2020 Norian Youth Connect Program
Reflections on the Baku and Sumgait Pogroms: 30 Years Later
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AMAA Shares the Joy of Christmas with over 11,000 Children Throughout Armenia, Artsakh
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Farm stand: 8am-6pm daily, mid-June to October 31st. Family-owned and operated for more than 25 years, 40km north of Kamloops on the scenic Yellowhead Highway at McLure Ferry Road. Easy access via left hand-turn lane. Grab a dozen of our famous corn when in season. Take a ferry ride over the North Thompson River. A full selection of B.C. fruit and fresh veggies are available. B.C. pottery, cookbooks and preserves for sale.


Figured out what I was doing wrong...!
If you want to know what I have, just ask to come visit.
Madness- problem was my ineptitude..!!! Didn't pay attention to the line under the new password telling me to verify there first..!
Anthraxx- Iwill check out the 2 Af tanks I have in schools and let you know. Thank you a bunch for the offer.


As part of the promotion F40 guaranteed PokerStars Sunday evening four million U.S. dollars prize pool for the regular world's largest online tournament. In the end it was well over seven million.
Hard to believe: 36,169 players paid the $ 215 buy-in, or qualified through one of the numerous satellites. This brought about 360,000,000 chips in play. But for the first three spots fell to 2.4 million dollars, far more than most online tournaments a week. The total prize pool amounted to exactly $ 7,233,800, -.
With this course, were also a number of members of professional teams. Best German player Sebastian Ruthenberg was at number 765 for $ 1446.76. Jan Heitmann was 1910th for $ 434.02, George Danzer was at number 5142 just so expensive.
Monday, March 8th, 201010:21This entry was posted on at and is filed under Best Casino. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.


Friday, December 7, 2018 | We are fast approaching the 128th Anniversary of the Massacre at Wounded Knee. This anniversary marks one of the most shameful and dreadful days in the history of America.
In 1986 three Lakota men decided they would ride their horses on the same path Chief Big Foot and his 350 followers took when they road from the Cheyenne River Reservation in the bitter winter of December 1890 to seek the protection of Chief Red Cloud on the Pine Ridge Agency.
Native Sun News Today, voted "Best of the Dakotas" by both the North and South Dakota Newspaper Associations, is the largest weekly newspaper on the Northern Plains. The most trusted news source covering Native American issues.
Now a special 30th-anniversary edition in both hardcover and paperback, the classic bestselling history The New York Times called "Original, remarkable, and finally heartbreaking...Impossible to put down."
Bury My Heart at Wounded Knee is Dee Brown's eloquent, fully documented account of the systematic destruction of the American Indian during the second half of the nineteenth century. A national bestseller in hardcover for more than a year after its initial publication, it has sold almost four million copies and has been translated into seventeen languages. For this elegant thirtieth-anniversary edition—published in both hardcover and paperback—Brown has contributed an incisive new preface.
/ August 2018 | Preaching on climate change matters for two primary reasons that are in tension with one another. First, preaching on climate change matters because people don't want to hear about it. Second, preaching on climate change matters because people know they need to take action to address it.
There are many reasons people give for not wanting to hear about climate change, especially in church. Here are a few: Living day to day is already hard enough. Church is supposed to give me rest and refreshment and to recharge me for the next week. Climate change is not going to affect me; it's someone else's problem. The challenge is too enormous; there's nothing I can do about it, so why should I think about it? I come to church to be inspired, not to be depressed. Climate change is a political issue; politics doesn't belong in church.
Jim Antal is a denominational leader, climate activist, author and public theologian, in addition to being an Associate Fellow at Vermont Law School's New Economy Law Center. He serves as Special Advisor on Climate Change to the General Minister and President of the United Church of Christ.
This article has been updated with comments from a climate scientist and a responsefroma NOAA spokeswoman.
December 3, 2018 | Critics are perhaps too quick to judge America's young people, citing declining SAT scores, obesity, drug overdoses, addiction to smart phones, bizarre alterations of personal appearance and high rates of (alleged) mental illness. It's just too easy to be annoyed at how some of the cashiers at the local grocery store seem unable to carry on a conversation or have chosen to mutilate their faces with pieces of metal. We are perhaps too quick to condemn the crazed behavior of young protesters in recent years without fully considering what our government, society and culture have done to these poor souls.
Let's begin at the beginning. Forty percent of Americans are now born out of wedlock. Single parent families are associated with a long list of social maladies.
Doug Lynn offers a compelling insight into how the collective establishment uses its narratives to keep its hold on power.
October 6, 2018 | It is a fact the election of Donald Trump exposed certain undeniable realities in the United States for those willing to see. Perhaps first and foremost of the various revelations is the bona fide existence of The Collective. Also known as the Uniparty or The Establishment, The Collective is comprised of the following: The Democratic Party, Republican's in Name Only (RINOs), Neo-conservatives (Neocons), the Mainstream Media, the Corporatocracy, globalists, elite bankers and unelected government bureaucrats and officials; also often referred to as The Deep State or Military Industrial Complex.